Computational quantum chemistry helps us to determine, calculate, and study new concepts, compounds, reactions and mechanisms. Such way is very useful with compounds that require exceptionally care in their handling, such as explosives, decreasing risk to persons testing and maintenance costs in service. Computational quantum chemistry is the ground of molecular modeling, on prediction the behavior of individual molecules within a chemical system. The molecular modeling let us to obtain the molecular characteristics comparable with experimental date. In this way the molecular structures of for positional isomers of 2,4,6-trinitrotoluene (TNT) were calculated by an ab initio HF/6-31G∗ method using self made local area personal computer (PC) cluster TAURAS. The cluster was made from heterogeneous commodity hardware of teaching class and for high performance computing (HPC) was used the SCore cluster system software developed in Japan. The structure and the features of the cluster are described and the performance is evaluated during solving of linear algebra testing tasks. During the determination of the structures of the positional isomers of TNT, the deformation of the phenyl ring and the distortions of the nitro and methyl groups were concern. The calculations confirmed that both of these were affected by the positions of nitro groups. A comparison of the calculated energies of all the isomers revealed the tendency to form the stable isomers when the close contact effects of the nitro groups were reduced.